The classical and quantum superintegrability of the \(n\) D anisotropic harmonic oscillator has been studied in [1]}. The quantization of the classical system is there obtained by introducing creation and annihilation operators. This technique is widely in use today (see for example [2]} and [3]}, where the anisotropic harmonic oscillator is generalized to 2D constant-curvature manifolds obtaining new classical and quantum superintegrable systems) and can have some application towards the quantization of extended systems.
